7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Talk title to be here (bold, 14 pt)

Y. Hagimori1, K. Obuse2, and M. Yamada3
1
Graduate School of Life and Environmental Science, Okayama University2 Graduate
School of Environmental, Life, Natural Science and Technology, Okayama University
3
Research Institute for Mathematical Sciences, Kyoto University
e-mail (speaker): obuse@okayama-u.ac.jp
Two-dimensional barotropic flow on a rotating

sphere is one of the simplest mathematicalmodels describing the dynamics of planetaryatmospheres. This model is very simple anddoes not take into account three-dimensional
fluid motion, planetary topography, or, in manycases, heat distribution for example.
Nevertheless, it exhibits rich fluid dynamics,
including the formation of large-scale zonal
flows[1,2,3,4]. This model also has the interesting
aspect that it has the same mathematicalstructureasthespecial
caseofHasegawa-Mima equation when a plane
approximation is applied to it.
In this talk, we consider unforced
two-dimensional turbulence on a rotating
sphere and discuss how the nonlinear
interactions of Rossby waves, which are wave
solutions unique to rotating systems, areinvolved in the formation of the large-scale
zonal flows (westward circumpolar flows inthis case. Fig. 1(A)). It is known that when therotation rate of the sphere is very high, thethree-wave resonance non-linear interaction ofRossby wave strongly dominates the dynamics
of the flow field[5,6]. However, it is not possible
totransfer energy to Rossby waves
corresponding to zonal flows (zonal Rossby
waves) directly by three-wave resonanceinteractions[7,8]. This means that the formationof zonal flows takes place by weakly existing
non-resonant interactions, but the details havebeen little understood. In particular, we still do
not know why the zonal flows that develop due
to non-resonant interactions consist of waves
that are capable of resonant interactions, rather
than waves that are incapable of non-resonantinteractions (Fig. 1(B))[8].
Based on our recent detailed numericalcalculations of energy transfer by Rossby wave

three-wave non-resonant interactions, we reportthat the formation of the westward circumpolar
flow is due to non-local energy transfer by
three-wave near-resonant interactions (specialcases of non-resonant interactions) (Fig. 2).

Figure 1: (A)At sufficiently large times, we observe
westward circumpolar flows around both poles in
unforced system. (B) We see strong energy accumulation
only to waves that are capable of resonant interactions
though the wave interactions giving energy to zonal
Rossby waves is non-resonant interactions.

Figure 2: Temporal mean of energy transfer to zonal
Rossby waves. (A) Near-resonant nonlinear interactionstransfer energy to zonal Rossby waves with low
wavenumber. (B) Non-local nonlinear interactionstransfer energy to zonal Rossby waves with low
wavenumber.
References[1] S. Yoden and M. Yamada, J. Atomos. Sci. 50, 631(1993)[2] S. Takehiro et al., J. Atmos. Sci. 64, 4084 (2007).
[3] T. Nozawa and S. Yoden, Phys. Fluids 9, 2081
(1997)[4] K. Obuse et al., Phys. Fluids. 22, 056601 (2010)[5] M. Yamada and T. Yoneda, Physica D 245, 1 (2013)[6] A. Dutrifoy and M. Yamada, In preparation.
[7] G. M. Reznik et al., Dyn. Atmos. Oceans 18, 235(1993).
[8] K. Obuse and M. Yamada, Phys. Rev. Fluids 4,024601 (2019)